Question

Calculate the speed of a galaxy emitting light of wavelength

5.48×107m5.48 \times 10 ^ { - 7 } \mathrm { m }

which when received on Earth is measured to have a wavelength of

5.65×107m5.65 \times 10 ^ { - 7 } \mathrm { m }

.

Solution

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We can use the following relation to find the speed of the galaxy

Δλλ=vc\frac{\Delta \lambda}{\lambda}=\frac{v}{c}

where (v)(v) is the speed of the galaxy and (c)(c) is the speed of light in space. Let's rearrange the relation to isolate (v)(v)

v=c×Δλλ=(3×108 m/s)×5.65×107 m5.48×107 m5.48×107 mv=c\times \frac{\Delta \lambda}{\lambda}=(3\times 10^{8} \mathrm{~ m/s}) \times \frac{5.65\times 10^{-7} \mathrm{~ m}-5.48\times 10^{-7} \mathrm{~ m}}{5.48\times 10^{-7} \mathrm{~ m}}

v=9.3×106 m/sv=9.3 \times 10^{6} \mathrm{~ m/s}

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